I have the Yamaha RX-V750 - basically the same as the 650 but with a couple of extra features, and compared it to the Denon 2105. I could hear the slight difference in tonal balance between the two that is usually described as the Yamaha being brighter and the Denon being warmer, but the difference was slight. With my speakers (older DefTech BP10s for the fronts, which have a silk-dome tweeter), I had a slight preference for the sound of the Yamaha. If I had newer DefTechs with the aluminum dome tweeters, the preference might have tipped the other way, since newer DefTechs are a bit brighter than the older models. I also thought that the Yamaha had a couple of other minor advantages, but that's pretty subjective. (Amber displays are obviously cooler than white/blue displays. Just kidding!)
I listen to movies pretty loud, but probably not as loud as some others. In my use (5.1 set-up), the 750 gets moderately warm, but never hot, and I have never experienced shut-down of any kind. My DefTechs are moderately efficient, 89 or 90 dB sensitivity, so they are more or less in the middle of the easy-to-drive vs. hard-to-drive continuum. And my room is big, with a cathedral ceiling, so I do have to turn up the volume pretty high.
For music, I am basically a 2-channel guy, most often using the Pure Direct mode. So the receiver stays pretty cool for music, even when I am blasting it. I can't comment on the thermal design of the Denon.
You're probably going to be pretty satisfied with either choice - but having the chance to live with both for a few days at home would be good.